phys 3380 - astronomy protostellar disks and jets – herbig haro objects disks of matter accreted...

PHYS 3380 - Astronomy

Protostellar Disks and Jets – Herbig Haro ObjectsDisks of matter accreted onto a protostar (“accretion disks”) often lead to the formation of jets (directed outflows; bipolar outflows)

- originate from the star and the inner parts of the disk and become confined to a narrow beam within a few billion miles of their source. - not known how the jets are focused, or collimated. Suggested that magnetic fields, generated by the star or disk, might constrain the jets.

When they strike interstellar medium/nebula - produce Herbig Haro Objects - small nebulae that fluctuate in brightness


Protostellar Disks and Jets – Herbig Haro Objects

HH34

Almost 50 years ago, George Herbig and Guillermo Haro independently discovered a number of compact nebulae with peculiar spectra near dark clouds.

- subsequently demonstrated that these objects were shock-excited nebulae. - shown that the large range of excitation conditions requires bow shocks and other complex morphologies.

By the early 1980s, several Herbig-Haro (HH) objects shown to be highly collimated jets of partially ionized plasma moving away from young stars at speeds of 100 to over 1000 km/s.

PHYS 3380 - Astronomy Stellar Jets

Of the 56 proplyds observed in the Orion nebula, 23 had visible jets.


Gases clumped - could provide insights into the nature of the disk collapsing onto the star.

Beaded jet structure "ticker tape" recording of how clumps of material have, episodically, fallen onto the star.

• jets "wiggle" along their multi-trillion-mile long paths, suggesting the gaseous fountains change their position and direction.

- might be evidence for a stellar companion or planetary system that pulls on the central star, causing it to wobble, which in turn causes the jet to change directions

• knots due to 'sputtering' of the central engine

Ubiquitous in the universe - occur over a vast range of energies and physical scales, in a variety of phenomena.

Stellar Jets

HH30


Protostellar Disks and Jets – Herbig Haro Objects

Herbig Haro Object HH30


XZ Tauri - young system with two stars orbiting each other - separated by about 6 billion kilometers (about the distance from the Sun to Pluto)

- shows bubble of hot, glowing gas extending nearly 96 billion kilometers from this young star system. - appears much broader than the narrow jets seen in other young stars, but it is caused by the same process - the ejection of gas from a star.

XZ Tauri

PHYS 3380 - Astronomy Evidence of Star Formation

Nebula around S Monocerotis:

Contains many massive, very young stars - O associations

Also includes T Tauri Stars – generally low mass stars, strongly variable; bright in the infrared - T associations

Fox Fur NebulaObserve regions containing young stars - must have formed recently

- lie between birth line and main sequence

Regions of star formation rich in dust and gas and contain IR protostars and stars still contracting toward the main sequence


Low-mass star formation in upper Scorpius- dashed lines evolutionary tracks of observed low-mass stars- all the low-mass PMS (pre-main sequence) stars have a mean age of about 5 Myr and show no evidence for a large age dispersion.- thin solid lines isochrones at 0.1, 0.3, 1, 3, 10, 30 Myr

Main Sequence


Evidence of Star Formation

The Cone NebulaOptical Infrared

Young, very massive star

Smaller, sunlike stars, probably formed under the influence of the massive star

Stellar formation itself triggers star evolutions - massive stars’ ionization fronts compress nearby gasses - trigger


Evidence of Star Formation

Star Forming Region RCW 38


Open Clusters of Stars

Large masses of Giant Molecular Clouds => Stars do not form isolated, but in large groups, called Open Clusters of Stars.

Open Cluster M7


Open Clusters of Stars

Large, dense cluster of (yellow and red) stars in the foreground; ~ 50 million years old

Scattered individual (bright, white) stars in the background; only ~ 4 million years old


Globules

~ 10 to 1000 solar masses;

Contracting to form protostars

Bok Globules:

PHYS 3380 - Astronomy GlobulesEvaporating Gaseous Globules (“EGGs”): Newly forming stars exposed by the ionizing radiation from nearby massive stars

- Shadows of the EGGs protect gas behind them, resulting in the finger-like structures at the top of the cloud.- Forming inside at least some of the EGGs are embryonic stars -- abruptly stop growing when the EGGs are uncovered - separated from the larger reservoir of gas from which they were drawing mass. Eventually emerge as the EGGs themselves succumb to photoevaporation.

The pillar is slowly eroding away by the ultraviolet light from nearby hot stars - "photoevaporation". As it does, small globules of especially dense gas buried within the cloud are uncovered.


Stellar Evolution

PHYS 3380 - Astronomy Stellar Types by MassBrown dwarfs (and planets): estimated lower stellar mass limit is 0.08 M (or 80MJup). Lower mass objects have core T too low to ignite H.

Red dwarfs: stars whose main-sequence lifetime exceeds the present age of the Universe (13.7x109 yr). Models yield an upper mass limit of stars that must still be on main-sequence, even if they are as old as the Universe of 0.7M

Low-mass stars: stars in the region 0.7 ≤ M ≤ 2 M . After shedding considerable amount of mass, they will end their lives as white dwarfs and possibly planetary nebulae.

Intermediate mass stars: stars of mass 2 ≤ M ≤ 8-10 M. Similar evolutionary paths to low-mass stars, but always at higher luminosity. Give planetary nebula and higher mass white dwarfs.

High mass (or massive) stars: M >8-10 M. Distinctly different lifetimes and evolutionary paths huge variation.

PHYS 3380 - AstronomyMaximum Masses of Main-Sequence Stars

h Carinae

(Eta Carinae)

a) More massive clouds fragment into smaller pieces during star formation.b) Very massive stars lose mass in strong stellar winds

Eddington limit - point where gravitational force can no longer balance the continuum radiation force outwards. Exceeding the Eddington limit - star initiates very intense driven stellar wind from its outer layers.

Example: h Carinae: Binary system of a 60 M and 70 M star. Dramatic mass loss; major eruption in 1843 created double lobes.

Mmax~ 100 solar masses

The Eddington Limit or Eddington luminosity

The point at which the luminosity emitted by a star or active galaxy is so extreme that it starts blowing off the outer layers of the object. i.e., the greatest luminosity that can pass through a gas in hydrostatic equilibrium, meaning that greater luminosities destroy the equilibrium.

- named after the British astrophyicist Sir Arthur Stanley Eddington - famous for confirming the general theory of relativity using eclipse observations. - Eddington limit is likely reached around 120 solar masses, at which point a star starts ejecting its envelope through intense solar wind. - Wolf-Rayet stars are massive stars showing Eddington limit effects, ejecting .001% of their mass through solar wind per year.


Minimum Mass of Main-Sequence Stars

Mmin = 0.08 M

At masses below 0.08 M, stellar progenitors do not get hot enough to ignite thermonuclear fusion.

Brown Dwarfs

Gliese 229B


Brown Dwarfs

Hard to find because they are very faint and cool; emit mostly in the infrared.

Many have been detected in star forming regions like the Orion Nebula.


The structure and evolution of a star is determined by the laws of

Main Sequence Stars

• Hydrostatic equilibrium - weight of each layer balanced by pressure

• Energy transport - energy moves from hot to cool

• Conservation of mass - total mass = sum of shell masses

• Conservation of energy - total luminosity = sum of shell energies

A star’s mass (and chemical composition) completely determines its properties.

Stars initially all line up along the main sequence

- in hydrostatic equilibrium - outward pressure of gas balanced by inward weight


Stellar Model

For isolated, static, and spherically symmetric stars – these laws lead to four basic equations to describe structure. All physical quantities depend on the distance from the centre of the star alone.

1) Equation of hydrostatic equilibrium: at each radius, forces due to pressure differences balance gravity

2) Conservation of mass: Total mass equals sum of shell masses - no gaps.

3) Conservation of energy : at each radius, the change in the energy flux = local rate of energy release

4) Equation of energy transport : relation between the energy flux and the local gradient of temperature

PHYS 3380 - AstronomySolving the Equations of Stellar StructureWe can derive four differential equations, which govern the structure of stars - provide set of coupled equations for determining stellar model.

r = radius = density at rP = pressure at rM = mass of material within rL = luminosity at r (rate of energy flow across sphere of radius r)T = temperature at rR = Rosseland mean opacity at r - opacity of gas of given composition, temperature, and density, averaged over the various wavelengths of the radiation being absorbed and scattered. = energy release per unit mass per unit time

P = P (, T, chemical composition)R = R(, T, chemical composition) -

= (, T, chemical composition)These quantities dependent on density, temperature, and chemical composition

€

dM(r)dr

= 4πr2ρ (r)

€

dP(r)dr

= −GM(r)ρ (r)r2

€

dL(r)dr

= 4πr2ρ (r)ε(r)

€

dT(r)dr

= − 3ρ(r)κ R (r)64πr2σT(r)3

L(r)


Boundary Conditions

Two of the boundary conditions are fairly obvious, at the centre of the starM=0, L=0 at r=0

At the surface of the star its not so clear, but we use approximations to allow solution. There is no sharp edge to the star, but for the the Sun (surface)~10-4 kg m-3. Much smaller than mean density (mean)~1.4103

kg m-3 (which we derived). We know the surface temperature (Teff=5780K) is much smaller than its minimum mean temperature (2106 K).

Thus we make two approximations for the surface boundary conditions:= T = 0 at r=rs

i.e. that the star does have a sharp boundary with the surrounding vacuum

PHYS 3380 - AstronomyUse of Mass as the Independent Variable

The preceding formulae would (in principle) allow theoretical models of stars with a given radius. However from a theoretical point of view it is the mass of the star which is chosen, the stellar structure equations solved, then the radius (and other parameters) are determined. We observe stellar radii to change by orders of magnitude during stellar evolution, whereas mass appears to remain constant. Hence it is much more useful to rewrite the equations in terms of M rather than r.

If we divide the other three equations by the equation of mass conservation, and invert the latter:

With boundary conditions:r=0, L=0 at M=0=0, T=0 at M=Ms

We specify Ms and the chemical composition and now have a well defined set of relations to solve. It is possible to do this analytically if simplifying assumptions are made, but in general these need to be solved numerically on a computer.

€

drdM

= 14πr2ρ

€

dLdM

= ε

€

dPdM

= − GM4πr4

€

dTdM

= − 3κ RL256π 2r4σT 3


The equations are not time dependent - we must iterate with the calculation of changing chemical composition to determine short steps in the lifetime of stars. The crucial changing parameter is the H/He content of the stellar core.

Stellar Evolution

So we can evolve a model using

The set of equations must be supplemented by equations describing the rate of change of abundances of the different chemical elements. Let CX,Y,Z be the chemical composition of stellar material in terms of mass fractions of hydrogen (X), helium, (Y) and metals (Z) [e.g. for solar system X=0.7,Y=0.28,Z=0.02]

€

∂(CX ,Y ,Z )M∂t

= f (ρ,T,CX ,Y ,Z )

€

(CX ,Y ,Z )M ,t0 +δt = (CX ,Y ,Z )M ,t0 +∂(CX ,Y ,Z )M

∂t

PHYS 3380 - AstronomyTheoretical Stellar Evolution Model

The outcome is a theoretical HR-diagram.

PHYS 3380 - Astronomy The Main-Sequence Phase

Pressure increases steeply in centre

- 50% of mass is within radius 0.25R- only 1% of total mass is in the convection zone and above

- no convective process in 99% of star - does not become fully mixed. - core becomes He rich.

Fusion is most efficient in the centre, where T ishighest.


Hipparcos satellite measured 105 bright stars with p>0.001" confident distances for stars with d<100 pc

Hertzsprung-Russell diagram for the 41704 single stars from the Hipparcos Catalogue with relative distance precision better than 20% and (B-V) less than or equal to 0.05 mag. Colors indicate number of stars in a cell of 0.01 mag in (B-V) and 0.05 mag in absolute magnitude (MV).

Notice the spread in stars on main sequence.

PHYS 3380 - Astronomy Evolution on the Main Sequence

Zero-Age Main

Sequence (ZAMS)

MS evolution

Main-Sequence stars live by fusing H to He.

- finite supply of H => finite life time.

As star evolves, H consumed, chemical composition changes (H/He ratio).

- total number of nuclei becomes less - pressurereduced- gravity - pressure stability unbalanced- core contracts - temperature and density increase and nuclear reaction rate increases- star becomes more luminous- additional energy flowing out forces outer layers to expand and cool

Star gradually becomes larger, brighter, and cooler

Slow changes cause star to move up and to the right on HRD - main sequence not a line but a band - Sun about 30% brighter than when at ZAMS

PHYS 3380 - Astronomy Lifetime on the Main Sequence

Dependent on mass

For the few main-sequence stars for which masses are known, there is a Mass-luminosity relation.

L Mn

Where n=3-5. Slope changes at extremes, less steep for low and high mass stars.

This is why the main-sequence on the HRD is a function of mass i.e. from bottom to top of main-sequence, stars increase in mass

• The mass-luminosity relation flattens out at higher masses, due to the contribution of radiation pressure in the central core. (This helps support the star, and decreases the central temperature slightly.) The relation also flattens significantly at the very faint end of the luminosity function. This is due to the increasing important of convection for stellar structure.• Main sequence stars also obey a mass-radius relation. This relation displays a significant break around 1M; R /Mξ, with ξ≈0.57 for M > 1M, and ξ≈0.8 for M < 1M. This division marks the onset of a convective envelope. Convection tends to increase the flow of energy out of the star, which causes the star to contract slightly. As a result, stars with convective envelopes lie below the mass-radius relation for non-convectivestars and also moves the star above the nominal mass-luminosity relation. • The depth of the convective envelope increases with decreasing mass. Stars with M≈1M have extremely thin convective envelopes, while stars with M < ~0.3M are entirely convective. Nuclear burning ceases around M≈ 0.08M. The region of nuclear energy generation is restricted to a very small mass range near the center of the star. The rapid fall-off of εn (energy release per unit mass per unit time) with radius reflects the extreme sensitivity of energy generation to temperature.• Stars with masses below ~ 1M generate most of their energy via the proton-proton chain. Stars with more mass than this create most of their energy via the CNO cycle. This changeover causes a shift in the energy transport in stellar interiors.


Lifetime on the Main SequenceA star’s life time T ~ energy reservoir / luminosity

Energy reservoir ~ M

Luminosity: L ~ M3.5

T ~ M/L ~ 1/M2.5

Massive stars have short lives.

Red dwarfs use fuel so slowly, should survive for 200 - 300 billion years - all still in infancy since age of universe 10 - 20 billion years


The Source of Stellar Energy

In the sun, this happens primarily through the proton-proton (PP) chain

Recall from our discussion of the sun:

Stars produce energy by nuclear fusion of hydrogen into helium.


The CNO CycleIn stars slightly more massive than the sun, a more powerful energy generation mechanism than the PP chain takes over:

The CNO Cycle.

Highly temperature dependent


Energy Transport Structure

Inner radiative, outer convective

zone

Inner convective, outer radiative zone

CNO cycle dominant PP chain dominant


Summary: Stellar Structure

MassSun

Radiative Core, convective envelope;

Energy generation through PP Cycle

Convective Core, radiative envelope;

Energy generation through CNO Cycle

• As a result of the extreme temperature dependence of CNO burning, those stars that are dominated by CNO fusion have very large values of L/4πr2 in the core. This results in convective instability and convective energy transport is extremely efficient.• Because of the extreme temperature sensitivity of CNO burning, nuclear reactions in high mass stars are generally confined to a very small region, much smaller than the size of the convective core.

- conditions under which a region of a star is unstable to convection is expresses by the Schwarzschild criterion:

where g is the gravitational acceleration, and Cp is the heat capacity. A parcel of gas that rises slightly will find itself in an environment of lower pressure than the one it came from. As a result, the parcel will expand and cool. If the rising parcel cools to a lower temperature than its new surroundings, so that it has a higher density than the surrounding gas, then its lack of buoyancy will cause it to sink back to where it came from. However, if the temperature gradient is steep enough (i. e. the temperature changes rapidly with distance from the center of the star), or if the gas has a very high heat capacity (i. e. its temperature changes relatively slowly as it expands) then the rising parcel of gas will remain warmer and less dense than its new surroundings even after expanding and cooling. Its buoyancy will then cause it to continue to rise. The region of the star in which this happens is the convection zone.

€

−dTdZ<gCp

phys 3380 - astronomy protostellar disks and jets – herbig haro objects disks of matter accreted...

Documents